What is the general solution for cos(θ)+2cos(θ+240)=1 ?

The general solution for cos(θ)+2cos(θ+240)=1 is θ=0.61547…+360n,θ=180-0.61547…+360n

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cos(θ)+2cos(θ+240)=1

cos (θ) + 2 cos (θ + 24 0^{\circ}) = 1

θ = 0.61547 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.61547 \dots + 36 0^{\circ} n

Solution steps

cos (θ) + 2 cos (θ + 24 0^{\circ}) = 1

Rewrite using trig identities

3 sin (θ) = 1

Subtract

1

from both sides

3 sin (θ) - 1 = 0

Move

1

to the right side

3 sin (θ) = 1

Divide both sides by

3

sin (θ) = \frac{3}{3}

Apply trig inverse properties

θ = arcsin (\frac{3}{3}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{3}{3}) + 36 0^{\circ} n

Show solutions in decimal form

θ = 0.61547 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.61547 \dots + 36 0^{\circ} n

arccos (x) = \frac{π}{8}

sin (θ) = 5

sin^{2} (x) = 4 cos (x)

- 8 cos (x) sin (x) = 0

0 = cot (x)

What is the general solution for cos(θ)+2cos(θ+240)=1 ?
The general solution for cos(θ)+2cos(θ+240)=1 is θ=0.61547…+360n,θ=180-0.61547…+360n